Also notice that in a precursor to this paper [1]},
using totally different techniques (basically
applications of the Logspace version of Courcelle's theorem [2]})
it was claimed that the number of Euler tours in bounded tree-width
directed and undirected graphs can be counted in Logspace but the approach had
a serious flaw in the undirected version. Later versions [3]}, [4]}
of the paper claim the result only for directed graphs. This work proves a
slightly weaker version of the result - the upper bound being #SAC\(^1\) rather
than Logspace.
